Teorema da Função Implícita e diferenciabilidade de soluções de EDO’s com relação a parâmetros

Abstract

In this work, we present the proof of the Differentiability Theorem of Solutions with Relation to Parameters using as main argument the Implicit Theorem Function in Banach spaces. To do that, it was necessary to study topics of metric spaces and calculus in Banach spa- ces, where we introduce the concept of Fréchet derivative. Finally, we combine the Implicit Function Theorem with Picard’s Theorem, in order to obtain the Theorem of Differentiation of Solutions with Relation to Parameters.